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| Initial and Boundary Value Problem for a System of Balance Laws from Chemotaxis: Global Dynamics and Diffusivity Limit |
| Zefu Feng,Jiao Xu,Ling Xue,Kun Zhao |
| (School of Mathematical Sciences, Chongqing Normal University,
Chongqing 400047, China;SUSTech International Center for Mathematics, Southern University
of Science and Technology, Shenzhen 518055, Guangdong, China;College of Mathematical Sciences, Harbin Engineering University,
Harbin 150001, Heilongjiang, China;Department of Mathematics, Tulane University, New Orleans,
LA 70118, USA) |
| DOI： |
| Abstract: |
| In this paper, we study long-time dynamics and diffusion limit of large-data solutions to a system of balance laws arising from a chemotaxis model with logarithmic sensitivity and nonlinear production/degradation rate. Utilizing energy methods, we show that under time-dependent Dirichlet boundary conditions, long-time dynamics of solutions are driven by their boundary data, and there is no restriction on the magnitude of initial energy. Moreover, the zero chemical diffusivity limit is established under zero Dirichlet boundary conditions, which has not been observed in previous studies on related models. |
| Key words: Balance laws, chemotaxis, initial-boundary value problem, dynamic boundary condition, strong solution, long-time behavior, diffusivity limit. |